EDIT: Also “rhino with grasshopper” >


Internet Research

“What colour is information?”   >  google   >

Color Is Information

Problem Summary

When color is used arbitrarily and gratuitously information is obscured.


The Function of Color

Properly used, color itself can convey information. It can reinforce typographic information, add to order and logic, indicate varying qualities and quanities, call attention and emphasize, establish tone or connotation, and clarify complex ideas. Generally speaking, use “neutral” colors like black, white, and greys to just present the facts with no particular “spin”, and use other colors sparingly to reinforce or enhance a message… As discussed in Colors In Context, colors change depending upon both physical and psychological situations.


  1. The Visual Display of Quantitative Information, Edward Tufte.


Colors In Context

Problem Summary

When the same color is used in different contexts the perception of that color can change radically.


On Color Theory

Color is a deep subject. Artists and designers spend a long time mastering color theory. Perhaps the world’s foremost master of color is Josef Albers, whose paintings are essentially case studies in color, demonstrating how the same color can look radically different (or even how two different colors can look the same) depending upon their contexts.


  1. Interaction of Color, Josef Albers, Yale University Press, New Haven, CT, 1975.
  2. Graphic Design for Electronic Documents and User Interfaces, chapter 4, Color, Aaron Marcus, ACM Press, 1992.
  3. Exploring Color in Interface Design, Subing, Falk & Johansen, Interactions magazine, July/August, 1996.

Colors For The Colorblind

Predecessor Patterns

. . . the importance of color in conveying a message is described in Color Is Information, and we know that color perception changes according to Colors In Context. Here we consider a special context for color information, the effects of colorblindness, color-deficiency or dyschromatopsia.

Problem Summary

Using colors that are confused by the eyes of colorblind (color-deficient or dyschromatopic) people will exclude a significant percentage of the population.



Most colorblindness is a genetic defect involving the X-chromosome which affects the approximately 6 million color-sensitive cells of the retina called cones. (Approximately 100 million light-sensitive cells called rods are responsible for night vision, etc.) Other causes include tumors, aneurisms and some diseases.Just as most “blind” people are not completely blind, most people who have deficient color perception are not completely “colorblind”. Hence, we hesitate to use the adjective, in favor of the more scientifically correct color-deficient or dyschromatopic. Regardlessly, the percentage of the population afflicted by this condition makes the problem non-trivial:

             Causasian   Asiatic     Others       Male  8.0%        5.0%        3.0%
     Female  0.5%        0.5%        0.5%

Normal color perception is trichromatic, i.e., consisting of the three primary colors of light (red, green and blue). Six general types of dyschromatopsia have been identified. People with complete colorblindness, a rare retinal defect affecting the cones of 0.003% of caucasian males, are achromatic, also known as monochromatic. People with partial colorblindness are either dichromatic or anonamlously trichromatic.

Dichromatic people are missing one of the color-sensitive photopigments in retinal cones, usually an inherited genetic condition. For example, when either the red- or green-sensitive pigment is missing, reds and greens are unable to be distinguished. Specifically, there are three kinds of dichromatic colorblindness, presented here with the percentages for caucasian males [1]:

    Protanopia missing red-sensitive pigment:  1.0%
Deuteranopia missing green-sensitive pigment:  1.1%
   Tritanopia missing blue-sensitive pigment:  0.001%

Anomalously trichromatic people have all three pigments, but one or more may be abnormal. This condition is more common than being dichromatic, accounting for nearly 6 of the 8% of caucasian males who are colorblind:

      Protanomalous abnormal red sensitivity:  1.0%
  Deuteranomalous abnormal green sensitivity:  4.9%


While designing for all forms of colorblindness may be difficult, we can construct some rules of thumb for using colors that people with dyschromatopsia can distinguish. In particular, since the majority of color-deficient people are red-green deficient, we can pay special attention to red-green confusion.


  1. Color Vision, Leo M. Hurvich, Sinauer Associates Inc., Sunderland, Mass., 1981.
  2. Color Theory and Its Application in Art and Design,, G. A. Agoston, Berlin: Springer-Verlag, second edition, 1987.
  3. Measuring Color, R. W. G. Hunt, New York: Halsted Press, 1987.

    Josef Albers

    Josef Albers (/ˈælbərz, ˈɑːl-/; German: [ˈalbɐs]; March 19, 1888 – March 25, 1976) was a German-born American artist and educator whose work, both in Europe and in the United States, formed the basis of some of the most influential and far-reaching art education programs of the twentieth century.

    Homage to the Square

    Josef Albers, Homage to the Square, 1965

    Accomplished as a designer, photographer, typographer, printmaker, and poet, Albers is best remembered for his work as an abstract painter and theorist. He favored a very disciplined approach to composition. Most famous of all are the hundreds of paintings and prints that make up the series, Homage to the Square. In this rigorous series, begun in 1949, Albers explored chromatic interactions with nested squares. Usually painting on Masonite, he used a palette knife with oil colors and often recorded the colors he used on the back of his works. Each painting consists of either three or four squares of solid planes of color nested within one another, in one of four different arrangements and in square formats ranging from 406×406 mm to 1.22×1.22 m.[12]

Impossibles (1931) dates from Albers’s years at the Bauhaus and represents his experiments with nontraditional materials and techniques. The mechanical means of producing such glass pieces allowed him to achieve the discipline and detachment that he considered necessary to create nonrepresentational forms. Like other artists of his generation, Albers moved from a figurative style of picture making to geometrically based abstraction. Homage to the Square: Apparition, painted in 1959, is a disarmingly simple work, composed of four superimposed squares of oil color applied with a palette knife directly from the tube onto a white, primed Masonite panel. It is part of a series that Albers began in 1950 and that occupied him for 25 years. The series is defined by an unmitigating adherence to one pictorial formula: the square. The optical effects Albers created—shimmering color contrasts and the illusion of receding and advancing planes—were meant not so much to deceive the eye as to challenge the viewer’s faculties of visual reception. This shift in emphasis from perception willed by the artist to reception engineered by the viewer is the philosophical root of the Homage to the Square series. Albers tried to teach the mechanics of vision and show even the uninformed viewer how to see. He was always proud that many nonart students took his classes at Yale.” Via



Knots & Polygons

Research expedition via Wikipedia, cut-and-paste.

Tessellation (computer graphics)

In computer graphics, tessellation is used to manage datasets of polygons (sometimes called vertex sets) presenting objects in a scene and divide them into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL and Direct3D 11.

In computer-aided design

In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces, edges, and vertices, constitute a continuous boundary of a 3D body. Arbitrary 3D bodies are often too complicated to analyze directly. So they are approximated (tessellated) with a mesh of small, easy-to-analyze pieces of 3D volume—usually either irregular tetrahedra, or irregular hexahedra. The mesh is used for finite element analysis.

Polygonal chain

In geometry, a polygonal chain is a connected series of line segments.

See also




Knot theory

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician’s knot differs in that the ends are joined together so that it cannot be undone.
A three-dimensional depiction of a thickened trefoil knot, the simplest non-trivial knot

A knot diagram of the trefoil knot



Archaeologists have discovered that knot tying dates back to prehistoric times. Besides their uses such as recording information and tying objects together, knots have interested humans for their aesthetics and spiritual symbolism. Knots appear in various forms of Chinese artwork dating from several centuries BC (see Chinese knotting). The endless knot appears in Tibetan Buddhism, while the Borromean rings have made repeated appearances in different cultures, often representing strength in unity. The Celtic monks who created the Book of Kells lavished entire pages with intricate Celtic knotwork.

Intricate Celtic knotwork in the 1200-year-old Book of Kells

A mathematical theory of knots was first developed in 1771 by Alexandre-Théophile Vandermonde who explicitly noted the importance of topological features when discussing the properties of knots related to the geometry of position. Mathematical studies of knots began in the 19th century with Gauss, who defined the linking integral (Silver 2006). In the 1860s, Lord Kelvin‘s theory that atoms were knots in the aether led to Peter Guthrie Tait‘s creation of the first knot tables for complete classification. Tait, in 1885, published a table of knots with up to ten crossings, and what came to be known as the Tait conjectures. This record motivated the early knot theorists, but knot theory eventually became part of the emerging subject of topology.

In the late 1970s, William Thurston introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Many knots were shown to be hyperbolic knots, enabling the use of geometry in defining new, powerful knot invariants. The discovery of the Jones polynomial by Vaughan Jones in 1984 (Sossinsky 2002, pp. 71–89), and subsequent contributions from Edward Witten, Maxim Kontsevich, and others, revealed deep connections between knot theory and mathematical methods in statistical mechanics and quantum field theory. A plethora of knot invariants have been invented since then, utilizing sophisticated tools such as quantum groups and Floer homology.

Chinese knotting

Eight examples of one traditional Chinese knot.

Chinese knotting (Chinese: 中國結; pinyin: Zhōngguó jié) is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960-1279 AD) in China. It was later popularized in the Ming). The art is also referred to as “Chinese traditional decorative knots”.[1] In other cultures, it is known as “decorative knots”.

Chinese knots are usually lanyard type arrangements where two cords enter from the top of the knot and two cords leave from the bottom. The knots are usually double-layered and symmetrical.

File:Thistlethwaite unknot.svg
This is a unknot described by Morwen Thistlethwaite.


…I find all this interesting because as with leads or yarn, the default state of loose strands seems to be tangled.